线性代数及其应用（第三版）（英文版） 下载 mobi epub pdf 电子书 2024

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介绍了线性代数最基本的概念、理论和证明。包含了大量与实际问题相关的习题，并附有习题答案。提供了丰富的应用以解释工程学、计算机科学、数学、物理学、生物学、经济学和统计学中的基本原理及简单计算。提出了矩阵-向量乘法的动态和图形观点，将向量空间的概念引入线性系统的学习中，介绍了正交性和最小二乘方问题。强调了在科学和工程学领域，计算机对线性代数发展和实践的影响。用小图标标记的部分可在网站www.laylinalgebra.com或www.mymathlab.com上找到相应的技术支持，包含习题的数据文件、实例学习和应用方案等内容。

 

 

内容简介

线性代数是处理矩阵和向量空间的数学分支科学，在现代数学的各个领域都有应用。本书主要包括线性方程组、矩阵代数、行列式、向量空间、特征值和特征向量、正交性和最小二乘方、对称矩阵和二次型等内容。本书的目的是使学生掌握线性代数最基本的概念、理论和证明。首先以常见的方式，具体介绍了线性独立、子空间、向量空间和线性变换等概念，然后逐渐展开，最后在抽象地讨论概念时，它们就变得容易理解多了。

 

 

目    录
CHAPTER 1  Linear Equations in Linear Algebra  1

Introductory Example: Linear Models in Economics and Engineering  1

1.1    Systems of Linear Equations 2

1.2    Row Reduction and Echelon Forms  14

1.3    Vector Equations  28

1.4    The Matrix Equation Ax = b  40

1.5    Solution Sets of Linear Systems  50

1.6    Applications of Linear Systems  57

1.7    Linear Independence  65

1.8    Introduction to Linear Transformations  73

1.9    The Matrix of a Linear Transformations  82

1.10    Linear Models in Business, Science, and Engineering  92

Supplementary Exercises  102

 

CHAPTER 2  Matrix Algebra  105

Introductory Example: Computer Models in Aircraft Design  105

2.1    Matrix Operations  107

2.2    The Inverse of a Matrix  118

2.3    Characterizations of Invertible Matrices  128

2.4    Partioned Matrices  134

2.5    Matrix Factorizations  142

2.6    The Leontief Input-Output Modes  152

2.7    Applications to Computer Graphics  158

2.8    Subspaces of Rn  167

2.9    Dimension and Rank  176

Supplementary Exercises  183

 

CHAPTER 3  Determinants  185

Introductory Example: Determinants in Analytic Geometry  185

3.1    Introduction to Determinants  186

3.2    Properties of Determinants  192

3.3    Cramer’s Rule, Volume, and Linear Transformations  201

Supplementary Exercises  211

 

CHAPTER 4  Vector Spaces  215

Introductory Example: Space Flight and Control Systems  215

4.1    Vector Spaces and Subspaces  216

4.2    Null Space, Column Spaces, and Linear Transformations  226

4.3    Linearly Independent Sets: Bases  237

4.4    Coordinate Systems  246

4.5    The Dimension of a Vector Space  256

4.6    Rank  262

4.7    Change of Basis  271

4.8    Applications to Difference Equations  277

4.9    Applications to Markov Chains  288

Supplementary Exercises  299

 

CHAPTER 5  Eigenvalues and Eigenvectors  301

Introductory Example: Dynamical Systems and Spotted Owls  301

5.1    Eigenvectors and Eignevalues  302

5.2    The Characteristic Equation  310

5.3    Diagonalization  319

5.4    Eigenvectors and Linear Transformations  327

5.5    Complex Eigenvalues  335

5.6    Discrete Dynamical Systems  342

5.7    Applications to Differential Equations  353

5.8    Iterative Estimates for Eigenvalues  363

Supplementary Exercises  370

 

CHAPTER 6  Orthogonality and Least Squares  373

Introductory Example: Readjusting the North American Datum  373

6.1    Inner Product, Length, and Orthogonality  375

6.2    Orthogonal Sets  384

6.3    Orthogonal Projections  394

6.4    The Gram-Schmidt Process  402

6.5    Least-Squares Problems  409

6.6    Applications to Linear Models  419

6.7    Inner Product Spaces  427

6.8    Applications of Inner Product Spaces  436

Supplementary Exercises  444

 

CHAPTER 7  Symmetric Matrices and Quadratic Forms  447

Introductory Example: Multichannel Image Processing  447

7.1    Diagonalization of Symmetric Matices  449

7.2    Quadratic Forms  455

7.3    Constrained Optimization  463

7.4    The Singular Value Decomposition  471

7.5    Applications to Image Processing and Statistics  482

Supplementary Exercises  444

 

Appendixes

A  Uniqueness of the Reduced Echelon Form  A1

B  Complex Numbers  A3

 

Glossary  A9

Answers to Odd-Numbered Exercises  A19

Index  I1

 

 

作者介绍
David C. Lay：美国奥罗拉大学学士，加州大学洛杉矶分校硕士、博士。自1976年起开始于马里兰大学从事数学的教学与研究工作，阿姆斯特丹大学、自由大学、德国凯撒斯劳滕工业大学访问学者，在函数分析和线性代数领域发表文章30余篇。

关联推荐
本书是介绍性的线性代数教材，内容翔实，层次清晰，适合作为高等院校理工科数学课的双语教学用书，也可作为公司职员及工程学研究人员的参考书。
目录
CHAPTER 1 Linear Equations in Linear Algebra 1 Introductory Example: Linear Models in Economics and Engineering 1 1.1 Systems of Linear Equations 2 1.2 Row Reduction and Echelon Forms 14 1.3 Vector Equations 28 1.4 The Matrix Equation Ax = b 40 1.5 Solution Sets of Linear Systems 50 1.6 Applications of Linear Systems 57 1.7 Linear Independence 65 1.8 Introduction to Linear Transformations 73 1.9 The Matrix of a Linear Transformations 82 1.10 Linear Models in Business, Science, and Engineering 92 Supplementary Exercises 102 CHAPTER 2 Matrix Algebra 105 Introductory Example: Computer Models in Aircraft Design 105 2.1 Matrix Operations 107 2.2 The Inverse of a Matrix 118 2.3 Characterizations of Invertible Matrices 128 2.4 Partioned Matrices 134 2.5 Matrix Factorizations 142 2.6 The Leontief Input-Output Modes 152 2.7 Applications to Computer Graphics 158 2.8 Subspaces of Rn 167 2.9 Dimension and Rank 176 Supplementary Exercises 183 CHAPTER 3 Determinants 185 Introductory Example: Determinants in Analytic Geometry 185 3.1 Introduction to Determinants 186 3.2 Properties of Determinants 192 3.3 Cramer’s Rule, Volume, and Linear Transformations 201 Supplementary Exercises 211 CHAPTER 4 Vector Spaces 215 Introductory Example: Space Flight and Control Systems 215 4.1 Vector Spaces and Subspaces 216 4.2 Null Space, Column Spaces, and Linear Transformations 226 4.3 Linearly Independent Sets: Bases 237 4.4 Coordinate Systems 246 4.5 The Dimension of a Vector Space 256 4.6 Rank 262 4.7 Change of Basis 271 4.8 Applications to Difference Equations 277 4.9 Applications to Markov Chains 288 Supplementary Exercises 299 CHAPTER 5 Eigenvalues and Eigenvectors 301 Introductory Example: Dynamical Systems and Spotted Owls 301 5.1 Eigenvectors and Eignevalues 302 5.2 The Characteristic Equation 310 5.3 Diagonalization 319 5.4 Eigenvectors and Linear Transformations 327 5.5 Complex Eigenvalues 335 5.6 Discrete Dynamical Systems 342 5.7 Applications to Differential Equations 353 5.8 Iterative Estimates for Eigenvalues 363 Supplementary Exercises 370 CHAPTER 6 Orthogonality and Least Squares 373 Introductory Example: Readjusting the North American Datum 373 6.1 Inner Product, Length, and Orthogonality 375 6.2 Orthogonal Sets 384 6.3 Orthogonal Projections 394 6.4 The Gram-Schmidt Process 402 6.5 Least-Squares Problems 409 6.6 Applications to Linear Models 419 6.7 Inner Product Spaces 427 6.8 Applications of Inner Product Spaces 436 Supplementary Exercises 444 CHAPTER 7 Symmetric Matrices and Quadratic Forms 447 Introductory Example: Multichannel Image Processing 447 7.1 Diagonalization of Symmetric Matices 449 7.2 Quadratic Forms 455 7.3 Constrained Optimization 463 7.4 The Singular Value Decomposition 471 7.5 Applications to Image Processing and Statistics 482 Supplementary Exercises 444 Appendixes A Uniqueness of the Reduced Echelon Form A1 B Complex Numbers A3 Glossary A9 Answers to Odd-Numbered Exercises A19 Index I1

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